Jernej MrovljeDepartment of Systems and Control, Jožef Stefan Institute

DISTORTION IMPACT ON A STEREO DISTANCE

10th International PhD Workshop on Systems and Control

A Young Generation Viewpoint

Hluboka, 25/9/09

INTRODUCTION

RESULTS

PROBLEM

REALIZATION

optical aberrations (distortion)

camera calibration distortion model

stereoscopy STEDIMAT application

experiment results

CONTENT

INTRODUCTION PROBLEM REALIZATION RESULTS

STEREOSCOPY Stereoscopy

1. a technique used for recording and presenting 3D images

2. the viewing or appearance of objects in or as if in three dimensions 

Charles Wheatstone (1838): first scientist who described “stereopsis”

“...the mind perceives an object of three dimensions my means of the two

dissimilar pictures projected by it on the two ritinæ ” (C.Cheatstone)

First stereoscopic images and stereoscope

nowadays IMAX 3D (Image MAXimum 3D)

INTRODUCTION PROBLEM REALIZATION RESULTS

RECORDING STEREOSCOPIC IMAGES1) Stereo camera2) Stereo attachment3) Camera and stereo slider*4) Stereo system (two single lens cameras joined

together)

(2)

(1)(3)

(4)

INTRODUCTION PROBLEM REALIZATION RESULTS

1947

2009

VEIWING STEREOSCOPIC IMAGES

parallel viewing (a) cross viewing (b)

anaglyph images (c) polarized images (d)

INTRODUCTION PROBLEM REALIZATION RESULTS

(a)

(b)

(c)

(d)

“STEDIMAT” APPLICATION STEreo DIstance MeAsuring Tool written in Matlab >> Matlab Compiler >> standalone application(*.exe)

INTRODUCTION PROBLEM REALIZATION RESULTS

THE CALCULATION OF OBJECT’S POSITION - DISTANCE

)(2

tan2 0

0

RL xx

BxD

B – stereo base

x0 – horizontal image resolution

φ0 – horizontal angle of view

xL – object’s position in the left image

xR – objects’ position in the right image

00

B

12

D

LS

1B 2B

Lx

D

Rx

RS

INTRODUCTION PROBLEM REALIZATION RESULTS

OPTICAL ABERRATIONS chromatic and spherical aberrations affect image quality only tangential and radial distortions affect image geometry radial distortion causes inward or outward displacement of a given image

point from its ideal location negative radial displacement >> barrel distortion positive radial displacement >> pincushion distortion

If the object in the image is displaced, the calculated distance is incorrect!

inexpensive cameras with wide-angle lenses suffer barrel distortion (Canon PowerShot A640)

tangential distortion is due to imperfect centering of the lens components

INTRODUCTION PROBLEM REALIZATION RESULTS

DISTORTION MODEL distortion can be compensated mathematically:

1. applying parametric distortion model

2. estimating distortion coefficients

3. correcting the distortion polynomial approximation model of the radial distortion (Brown):

calibration procedure was done using “Camera Calibration Toolbox for Matlab”

toolbox uses Brown’s distortion model known as “Plumb Bob”

...753

321 rkrkrkrrd

xykyrk

xrkxyk

y

xrkrkrk

y

x

cc

ccccc

d

d

)4(2)2)(3(

)2)(4()3(2))5()2()1(1(

22

22642

RADIAL DISTORTION TANGENTIAL DISTORTION

INTRODUCTION PROBLEM REALIZATION RESULTS

each camera was calibrated separately a sequence of 20 images of the calibration board was taken in different

orientations

CALIBRATION PROCESS

in each image a set of calibration points were automatically detected

using the coordinates of the distorted and undistorted calibration points, the distortion parameters kc were calculated

INTRODUCTION PROBLEM REALIZATION RESULTS

CALIBRATION RESULTSleft camera right camera

centre of the image: displacement < 10px corners of the image: displacement > 100px

INTRODUCTION PROBLEM REALIZATION RESULTS

CORRECTING THE DISTORTION #1 distortion model was used to build “distortion-correction function” (DCF)

as a part of Stedimat for each distance DCF has to be applied twice:

1. using image point of the object’s location in the left image (xL)

2. using image point of the object’s location in the right image (xD)

INTRODUCTION PROBLEM REALIZATION RESULTS

“EXPERIMENT”/equipment: stereoscopic system with 2 digital cameras Canon PowerShot A640 StereoData Maker was used to synchronize cameras

CORRECTING THE DISTORTION #2“EXPERIMENT”:

7 test objects positioned at the distance D (30, 40, 50 and 60m) >>> four sets of stereoscopic images

image resolution: 3648x2736, focal distance: 35mm, stereo base: 0.56m, reference object : test object no.4

INTRODUCTION PROBLEM REALIZATION RESULTS

0

D

x

y

23 4 5

61 7

distance to each test object was calculated twice: undistorted/distorted image

CORRECTING THE DISTORTION #2EXPERIMENT:

7 test objects positioned at the distance D (30, 40, 50 and 60m) >>> four sets of stereoscopic images

image resolution: 3648x2736, focal distance: 35mm, stereo base: 0.56m, reference object : test object no.4

INTRODUCTION PROBLEM REALIZATION RESULTS

0

D

x

y

23 4 5

61 7

distance to each test object was calculated twice: 1–distorted image points, 2-distortion-free image points

RESULTS #1

INTRODUCTION PROBLEM REALIZATION RESULTS

RESULTS #2

INTRODUCTION PROBLEM REALIZATION RESULTS

RESULTS #3

INTRODUCTION PROBLEM REALIZATION RESULTS

RESULTS #4

INTRODUCTION PROBLEM REALIZATION RESULTS

DISTORTED IMAGE POINTSTest

objectDref=30m Dref=40m Dref=50m Dref=60m

1 4,3 3,9 7,0 5,62 4,3 3,8 7,0 5,63 2,9 3,8 4,8 5,64 0 (reference point)5 3,1 6,4 8,1 6,46 6,4 8,7 14,2 17,67 11,7 16,2 28,9 31,5

DISTORTION-FREE IMAGE POINTSTest

objectDref=30m Dref=40m Dref=50m Dref=60m

1 1,5 0,5 1,9 0,52 3,3 1,8 4,4 1,63 2,2 2,5 3,0 3,14 0 (reference point)5 0,5 1,9 2,8 0,56 1,1 1,7 1,1 1,27 5,3 8,0 2,3 3,4

RESULTS (absolute distance error [%])

INTRODUCTION PROBLEM REALIZATION RESULTS